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J. Phys. Chem. 1996, 100, 18292-18299
FEATURE ARTICLE Spin Catalysis of Chemical Reactions A. L. Buchachenko*,† and V. L. Berdinsky‡ Institute of Chemical Physics, Moscow 117334, Russia, and Institute of Chemical Physics in ChernogoloVka, Moscow Region 142432, Russia ReceiVed: April 3, 1996; In Final Form: August 22, 1996X
The spin catalysis of chemical reactions is a physical phenomenon of spin transformation of chemically reactive species induced by the exchange interaction of these species with external spin carriers. It manifests itself in the radical pair recombination, cis-trans isomerization of molecules with double bonds, recombination of spin-polarized and spin-aligned hydrogen atoms at cryogenic temperatures, etc. The theory and quantitative kinetics of spin catalysis in three- and four-spin systems are considered. Quantitative hierarchy of spin carriers with respect to their spin catalytic efficiency is discussed.
Introduction
SCHEME 1: Spin Chemistry. General Scheme
Spin chemistry as a new field of modern chemistry is concerned with electron and nuclear spins and with their behavior in chemical reactions. It is based on the fundamental principle: chemical reactions are allowed only for such spin states of the products whose total electron spin is identical with that of the reagents and are forbidden if they require a change of spin.1-3 The conservation of the total spin in chemical reactions results in electron and nuclear spin selectivity and differentiation of the chemical reactivity of reagent spin states. All phenomena in spin chemistry may be exemplified by the radical pair, which plays in spin chemistry a key role similar to that of the hydrogen molecule in quantum chemistry. Interactions of three types are able to change the electron spin and transform the spin forbidden, nonreactive triplet spin states of the radical pair into the spin-allowed, chemically reactive singlet state or Vice Versa (Scheme 1). Magnetic interactions of the electron spin with nuclear spins and with tht external magnetic field, Fermi and Zeeman interactions, are the sources of the magnetic effects of the first generation: MFE, magnetic field effect;4 MIE, magnetic isotope effect;5 CIDNP, chemically induced dynamic nuclear polarization;6 CIDEP, chemically induced electron spin polarization.7 Resonant microwaves produce the spin conversion of the radical pair and stimulate the magnetic effects of the second generation: RYDMR, reaction yield detected magnetic resonance;8 RIMIE, radioinduced magnetic isotope effect;9 SNP, stimulated nuclear polarization.10 Lastly, exchange interaction of the radical pair electron spins with the electron spin of a foreign spin carrier (radical, ion, paramagnetic molecule, etc.) provokes the magnetic effect of the third generation: SC, spin catalysis (see Scheme 1). The remarkable feature of this magnetic phenomenon is that the spin transformation of the radical pair is induced by nonmagnetic exchange interaction. The purpose of the present paper is to present an overview of the chemical manifestations and physics of this new phenomenon in spin chemistry. †
Institute of Chemical Physics. Institute of Chemical Physics in Chernogolovka. X Abstract published in AdVance ACS Abstracts, October 1, 1996. ‡
S0022-3654(96)01008-8 CCC: $12.00
Spin Catalysis: Experimental Evidence The first direct experimental demonstration of spin catalysis by radicals has been obtained in the photolysis of d,l-2,4diphenylpentan-3-one (DPP) in the presence of the stable nitroxide radical TEMPO, which is known to be a very powerful scavenger of carbon-centered radicals.11 The recombination probability, Pr, of the triplet sec-phenethyl/ sec-phenethylacyl radical pair generated in the photolysis of DPP by Norrish R-cleavage in benzene was unexpectedly shown to increase 3-fold as the concentration of TEMPO increases from 0 to 0.15 M. The dependence of Pr on the concentration of TEMPO is shown in Figure 1. These results contrast with the observation that the addition of diamagnetic scavengers, such as dodecanethiol, decreases the recombination probability Pr and demonstrate that a paramagnetic scaVenger catalyzes the radical recombination exhibiting a nontraditional spin catalytic effect. What is even more impressive is that the catalytic effect dominates over the traditional scavenging function of nitroxides. This is the reason that this new phenomenon was at first defined as an antiscaVenging effect.11 This amazing inversion, transformation of the radical scavenger into the radical catalyzer, is the result of the competition of two processes: the chemical scavenging of geminate radicals, partners of the triplet radical pair, by nitroxide and the spin exchange between geminate radicals and nitroxide. The former is expected to decrease Pr; the latter stimulates triplet-singlet conversion of the radical pair and, consequently, increases Pr. Both processes occur in a radical triad consisting of a radical pair and a third radical. The average exchange distance was © 1996 American Chemical Society
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J. Phys. Chem., Vol. 100, No. 47, 1996 18293 SCHEME 2: Nitroxide Biradicals with Spin Catalytic Function
Figure 1. of the recombination probability P of the triplet secphenethylacyl radical pair generated by photolysis of d,l-DPP in benzene as a function of 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) radical concentration.11
experimentally found to be 2-3 times larger than the hardsphere encounter distance so that the exchange interaction in the triad makes spin conversion in the radical pair at distances much larger than that of hard-sphere chemically reactive encounters.12 This is why the spin catalytic function of the third radical in a triad dominates over the chemical scavenging. The kinetic evidence of the spin catalytic effect in the recombination of carbon-centered radicals with nitroxide biradicals was reported by Buchachenko et al.13 The reaction scheme of scavenging alkyl radicals by the nitroxide biradical includes two subsequent reactions 2kB
B + R 98 M kM
M + R 98 stable product which implies the first addition of alkyl radical R to one of the biradical termini, which transforms biradical B into a monoradical M. The following addition of alkyl radical to nitroxide monoradical M results ultimately in a diamagnetic product. This reaction sequence was confirmed experimentally by ESR: the decay of biradicals was followed by the appearance of monoradicals, which manifests itself in the transformation of the ESR spectra of biradical to monoradical. The rate constant kB refers to one monoradical fragment of the biradical so that in order to compare the chemical reactivity of nitroxide moieties in biradicals and monoradicals, we should appeal to the rate constant ratio kB/kM, which can be measured experimentally. These ratios for biradicals of varying chemical structure (Scheme 2) are summarized in Table 1.13 Intuitively, the ratio kB/kM is expected to be equal to 1, taking into account only the chemical consideration. However, as is seen from Table 1, in all cases kB/kM > 1, i.e., the chemical reactivity of the nitroxide radical toward scavenging of the alkyl radical appears to depend on the presence of the second spin within the biradical molecule. The presence of the second spin accelerates the first recombination of a nitroxide fragment in the biradical with an alkyl radical by 10-50% vs second recombination. Therefore, the second radical terminus in the biradical cannot be considered as a passive spectator; it stimulates the recombination reaction of the first radical terminus. Analysis of different plausible reasons (mechanistic, steric, chemical factors, spin statistics, etc.) for this effect leaves the spin catalysis as the most probable concept. In the encounter pair of the alkyl radical with one of the biradical termini the ratio of populations of singlet and triplet spin states is 1:3, i.e.,
TABLE 1: Values of kB/kM for the Reaction of Biradicals with the Cyanoisopropyl Radical CH(CH3)2CN at 60 °C and the sec-Phenethyl Radical CH(CH3)Ph at 80 °C CH(CH3)2CN biradical
dioxane
I II III IV V VI
1.1 1.5
ethylbenzene
CH(CH3)Ph dioxane
ethylbenzene
1.2 1.5 1.1 1.3 1.3
1.4 1.2 1.0
1.3 1.3
only 25% of the encounter pairs are spin allowed to recombine. However, the exchange interaction of the second biradical terminus with radical partners in the reactive encounter pair induces triplet-singlet conversion in the pair and opens an additional recombination channel that is absent in the reaction of a nitroxide monoradical with an alkyl radical. Spin catalysis by paramagnetic lanthanide ions was reported by Turro et al.14a in the photolysis of p-methyl-substituted dibenzyl ketone in SDS micelles:
where A ) PhCH2 and B ) p-CH3PhCH2. The yield of the cage product AB, identified as a cage effect, was shown to increase as the concentration of lanthanide ions increases (Figure 2). The cage effect refers to the recombination of the secondary radical pair of alkyl radicals A and B originating from the primary radical pair by decarbonylation and is identical with the recombination probability P of this pair. As will be shown later, it is the SC effect that is responsible for the increasing P in the presence of lanthanide ions (Figure 2). The similar effects of the influence of lanthanide ions on the radical recombination were also recorded by other authors.14b-e Three-Spin Model Certainly, in radical triads all three radicals are participants of the chemical event, and the chemical behavior of the triad is controlled by spin dynamics induced by pairwise exchange interactions in a three-spin system. As a model for testing three-spin dynamics, we consider a radical triad (R1, R2, R3) in which one of the radical, R3, is supposed to be a spin catalyzer, but two others, R1 and R2, are treated as a radical pair born initially in the singlet or triplet spin state. The radical R3 is in the neighborhood of the radical pair (R1, R2) and couples with both partners R1 and R2 physically
18294 J. Phys. Chem., Vol. 100, No. 47, 1996
Buchachenko and Berdinsky
Figure 3. Spin states of the radical triad (R1, R2, R3). Dotted arrows indicate the oscillations between doublet spin states induced by the difference of the exchange energies ∆J ) J13 - J23. They produce triplet-singlet oscillatory time evolution of the selected radical pair (R1, R2).
Figure 2. Dependence of the cage effect (CE) and recombination probability P on the concentration of lanthanide ions.14 Ci is the ion concentration in micellar solution, Cmph is that in micellar phase, and ni is the average number of ions attached to an individual micelle. For the Eu3+, La3+, and Lu3+ ions the small dependene of CE and P on the concentration of ions is due to the ion-induced change of the size and structure of the micelle rather than to the spin catalysis.
or chemically. The reaction product R1R2 is presumably formed from the pair (R1, R2) in the singlet state. This claim has been confirmed experimentally many times1-3 and is valid for any radical pair (R1, R2), (R1, R3), and (R2, R3). However, we will focus on the generation probability of a selected molecule R1R2 in the triad (R1, R2, R3). When hyperfine and Zeeman energies are ignored, an approximation that is valid for radicals without magnetic nuclei at zero magnetic field, the spin Hamiltonian H of the radical triad can be written as
pH ) -pJ12(1/2 + 2S1S2) - pJ13(1/2 + 2S1S3) pJ23(1/2 + 2S2S3) (1) where Jij are the pairwise exchange energies for the pairs of radicals Ri and Rj (i * j) and Si are the spin operators for the unpaired electrons of these radicals (i ) 1, 2, 3). The radical triad as a three one-half spin system is characterized by a set of eight spin functions that should be eigenvectors of the total spin operator S, which is equal to S ) 3/2 (quartet state) or S ) 1/2 (doublet states), and the spin projection operator Sz. The quartet states Sz ) (3/2, (1/2 are degenerate, and their energy is -p(J12 + J13 + J23). The remaining four states with the total spin S ) 1/2 are split into two groups of doublets: two states with Sz ) +1/2 and two states with Sz ) -1/2 (Figure 3). Their energies are indicated in Figure 3 where
Ω ) {(1/2)[(J12 - J13)2 + (J12 - J23)2 + (J13 - J23)2]}1/2 (2) For the quartet states, as well as for any completely symmetric state of highest multiplicity in multispin systems, any pair recombination is spin forbidden if it results in a diamagnetic molecule. For such radical triads the spin state of any pair (Ri,
Rj) is the noncoherent mixture of triplet states exclusively. Therefore, neither the geminate reaction R1 + R2 nor the scavenging reactions R1 + R3 and R2 + R3 occur. These quartet triads may disappear by destruction only, and they are not the subject of spin catalysis. Only doublet states are exposed to spin catalysis: the doublet-doublet spin evolution, which conserves Sz ) +1/2 and Sz ) -1/2, is the only feasible dynamic spin process in the radical triad. The initial spin state of the radical triad (R1, R2, R3) composed of the correlated radical pair (R1, R2) in S or T states and nonpolarized radical catalyzer R3 is not the eigenvector of the spin Hamiltonian (1); it is the coherent mixture of these eigenvectors. Therefore, this state has to evolve obeying the Schro¨dinger’s equation. This spin evolution is determined by the spin Hamiltonian (1) and is governed by intratriad exchange interactions. The doubletdoublet spin evolution of the radical triad (R1, R2, R3) is inevitably accompanied by S-T conversion of the radical pair (R1, R2). The recombination rate of the radical pair (R1, R2) is T (t) of finding the pair in the proportional to the probability FSS T (t) takes the singlet state. For the initial triplet radical pair FSS 15 form T FSS (t) ) (∆J/(2Ω))2 sin2 Ωt
(3)
This is a fundamental equation that demonstrates that the doublet-doublet evolution in the radical triad (R1, R2, R3) is accompanied by the oscillating S-T conversion in the selected radical pair (R1, R2). Both conjugated processes, the doubletdoublet evolution of the radical triad and the triplet-singlet conversion of the selected radical pair, keep the spin projection Sz ) +1/2 and Sz ) -1/2 of the radical triad unchanged. Therefore, the spin evolution in the radical triad, which conserves S and Sz, is equivalent to the oscillating migration or “flowing” of the pair spin states (S, T, or their mixture) between the radical pairs, the components of the triad. The S-T evolution frequency Ω is determined by the combination of differences between the exchange energies of radical partners (eq 2), and the amplitude of oscillations is a function of the exchange energy difference ∆J ) J13 - J23 between the radical catalyzer R3 and radical partners R1 and R2 of the radical pair. Neither doublet-doublet evolution of the triad nor the singlettriplet conversion of the selected radical pair are conceivable if J13 ) J23; this is the case of the locked spin system. An asymmetric spin exchange (∆J * 0) between the radical pair partners and the radical R3 can be similarly proved to determine the spin evolution of the initially singlet radical pair (R1, R2). The probability for the pair to survive in a singlet
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J. Phys. Chem., Vol. 100, No. 47, 1996 18295
Figure 4. Vector model demonstrates the triplet-singlet conversion of the selected radical pair (R1, R2), induced by exchange interaction J23 in the radical triad (R1, R2, R3).
carbene, or metal ion, in principle is similar to that of threespin triads. Sixteen spin states of the triad are split into three groups: five states with total spin S ) 2, nine states with S ) 1, and two states with S ) 0. Only triplet states are subjected to spin catalysis, i.e., their spin evolution is induced by the exchange interaction. These nine states |S,Sz〉 are constructed of linear rp 〉, |Sc〉 combinations of the individual spin functions |Srp〉, |T0,( c rp rp and |T0,(〉, where |S 〉 and |T0,(〉 describe singlet and triplet c 〉 refer to singlet and states of the radical pair, and |Sc〉 and |T0,( triplet states of the catalyzer C. Spin orientations in the triad can be easily imagined from the presentation of spin vectors of these nine states |S,Sz〉: c c rp c rp c |1,1〉1 ) |SrpT+ 〉, |1,1〉2 ) 2-1/2|T0rpT+ - T+ T0〉, |1,1〉3 ) |T+ S〉
spin state obeys the equation15
|1,0〉1 ) |SrpT0c〉, T FSS (t)
) 1 - 3(∆J/(2Ω)) sin Ωt 2
2
(4)
which indicates that the initial singlet pair (R1, R2) in the radical triad (R1, R2, R3) oscillates between singlet and triplet states with the frequency Ω. Again, such a spin conversion takes place only if J13 * J23. Since the average value sin2 Ωt ) 1/2, then some part of the radical pairs njT ) 1 - (3/8)∆J2/Ω2 is the triplet state and another part njS ) 1 - (3/8)∆J2/Ω2 remains in the singlet state. Thus, the exchange interaction between the radical R3 and the partners of the pair (R1, R2) decreases the population of the initial singlet pairs in the triad, transforming them into the triplet ones. Thus, radical R3, being the spin catalyzer for the triplet radical pairs, appears to be the inhibitor for the initial singlet pairs, retarding the rate of the geminate recombination and decreasing the yield of the reaction product. Spin exchange can be visually represented as the precession of two spin vectors S1 and S2 around the direction of the total vector S1 + S2.16 In accordance with such a vector representation the spin exchange in the radical triad (R1, R2, R3) and the spin oscillation in the radical pair (R1, R2) can be imagined as follows. Suppose that the initial spin state of the radical triad is such as shown in Figure 4a. The selected radical pair (R1, R2) is in the state |T+〉 ) |R1R2〉, and both spins are oriented up, while the spin of the radical R3 is directed down. Assume now that the exchange interaction J23, which relates electron spins of radicals R1 and R3 and induces precession of spins S2 and S3 around the total spin S2 + S3, is switched on (Figure 4b). The interchange between the orientations of spins S2 and S3 after a time τ, such as J23τ ) π, transforms the pair spin state in such a way that the triad is now in a modified spin state when the radical pair (R1, R2) is fixed in the singlet state. The change of the radical pair spin is compensated by the reorientation of the spin of the radical R3 (Figure 4c). Thus, the spin exchange between radical partners in the triad can be described by the vector model as the dephasing of radical spin precessions. It is absolutely clear that if both radicals in the pair (R1, R2) are influenced by the exchange interaction with R3, then the rate of dephasing is governed by the combination of exchange energy differences Ω according to eqs 3 and 4. It is remarkable that this picture resembles the triplet-singlet spin conversion in an isolated radical pair; the only difference is that the latter is induced by the difference of Fermi and Zeeman interactions.1
rp c rp c |1,0〉2 ) 2-1/2|TT+ - T + T-〉, |1,0〉3 ) |T0rpSc〉
c c rp c rp c 〉, |1,-1〉2 ) 2-1/2|T0rpT- TT0〉, |1,-1〉3 ) |TS〉 |1,-1〉1 ) |SrpT-
}
(5)
Zero field splitting in C as well as dipolar, hyperfine, and Zeeman interactions strongly complicate the spin dynamics in the triad. However, being interested in spin catalytic effects only, we can ignore all magnetic couplings except exchange interactions. In this approximation some of the triad spin states (eq 5) are involved in the spin evolution, which transforms the states with the singlet radical pair |Srp〉 into those with triplet rp (or Vice Versa). The change of spin in the radical states |T0,( pair is compensated by the change of the spin projection SzC of the catalyzer C so that such a spin evolution changes neither the total spin S nor its projection Sz of (R1, R2, C). It is worthy to note that any interactions of two equiValent electron spins of the spin catalyzer C with partners of the radical pair (R1, R2) are not able to change spin multiplicities of C. Therefore, the exchange interaction within C may be ignored. Physically, spin dynamics in four-spin triads resembles the spin evolution in the three-spin model. The probability of T was finding the initial triplet radical pair in the singlet state FSS 17 shown to obey the equation T FSS (t) ) (4/3)(∆J/(2Ω))2 sin2 Ωt
(6)
which is similar to eq 3 for the three-spin system. Here, 2Ω is the energy splitting between the eigenvalues of the Hamiltonian of the four-spin triad (R1, R2, C) corresponding to oscillating triplet states in which a radical pair is in the singlet and triplet states,
2Ω ) {[J12 - JΣ]2 + 2(∆J)2}1/2
(7)
where J12 is the exchange potential between the partners of the radical pair, JΣ ) (J1C + J2C)/2, and J1C and J2C are the exchange potentials between the spin catalyzer C and each of the partners of the radical pair. It follows from eq 7 that the frequency of spin oscillation is determined by the combination of pairwise exchange potentials in the triad, while the amplitude of the oscillation is controlled by the difference ∆J ) J1C - J2C. Again, we conclude that the driving force of the spin catalysis in the four-spin system is the difference of the exchange energies between the catalyzer C and each of two radicals of the radical pair.
Four-Spin Model Spin dynamics in four-spin triads (R1, R2, C) composed of a radical pair (R1, R2) and a third partner C, which is supposed to be a biradical triplet molecule (oxygen, for instance), triplet
Chemical Dynamics of Spin Triads Spin oscillations in the selected radical pair modulate the chemical reactivity of the pair and consequently influence the
18296 J. Phys. Chem., Vol. 100, No. 47, 1996
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SCHEME 3: Two Competitive Pathways of the Radical Triad Transformation
chemical dynamics of triads. To elucidate what new kinetic effects are expected to follow from the spin catalysis, we consider the kinetic behavior of the instantly prepared ensemble of radical triads (R1, R2, R3) (Scheme 3). The triad is supposed to undergo spin catalytic recombination, generating the molecule R1R2 with the rate constant w. This spin dependent process is expected to compete with the spin independent destruction (via the radical escape, for instance) of the triad with the rate constant k. Since the molecules R1R2 are formed exclusively from radical pairs in singlet state, the yield Y(t) of the reaction product R1R2 obeys the equation
Y(t) ) w∫0 FSS(t) dt t
(8)
where FSS(t) is the singlet state related to the diagonal element in the density matrix of the radical pair in the triad, i.e., the probability for the pair to be in the singlet state. The latter can be derived from the density matrix of the radical triad F, which is the solution of the evolution equation
dF/dt ) -i[H,F] - (w/2){PS12F + FPS12} - kF
(9)
The first term represents the spin dynamics of triads induced by the spin Hamiltonian H, which includes pairwise exchange interactions. The second one describes the leakage of the triads due to the spin dependent recombination of the pairs (R1, R2). PS12 is the projection operator selecting the singlet spin state of pairs. The last term characterizes the decay of the triads via spin independent processes with the total rate constant k. Solutions of eq 9 for the different kinetic regimes have been summarized in ref 18. The most characteristic feature of the solutions can be illustrated by the particular case of weakly recombining radicals, i.e., when w , k. With this condition from eq 9 it follows that T (t) exp(-kt) FSS(t) ) FSS
(10)
T (t) and substituting eq 10 into eq 8, one Using eq 3 for the FSS can derive the kinetic equation for the yield of reaction product R1R2:
Y(t) ) Y∞[1 - (1 + Θ2) e-kt + Θ2 e-kt cos(2Ωt + φ)/cos φ] (11) where
Y∞ ) Y(t f ∞) ) (w/(2k))[(∆J/(2Ω))2/(1 + Θ2)], Θ ) k/(2Ω), φ ) arctan Θ, cos φ ) Θ/(1 + Θ2)1/2 (12) It is evident that the product yield of the spin catalytic reaction depends on rate constants k and w characterizing the chemical dynamics, as well as on parameters ∆J and Ω regulating the spin dynamics. From eq 11 it follows that the kinetics of spin-catalyzed reaction consists of two additive parts, and the second contribution oscillates in time according to eq 11. These oscillations, or quantum beats, in the rate and the reaction yield arise from the triplet-singlet conversion of the selected radical pair in the
Figure 5. Kinetics of the accumulation of the geminate recombination product R1R2 in the presence of spin catalyzer R3 at w , k and parameters (k/(2Ω)) ) 0.1 (1), 0.5 (2), 1.0 (3), and 5.0 (4).
triad and are similar to those in an isolated radical pair.19 The only difference is that the oscillations from an isoloated radical pair are induced by Fermi and Zeeman interactions, while those of the selected pair in the triad are stimulated by exchange interactions. An example of these beats is shown in Figure 5. At Ω . k, i.e., when the oscillation frequency is higher than the decay frequency, quantum beats are clearly seen. In the case of slow oscillations, Ω e k, quantum beats are not pronounced, since the main contribution into the kinetics goes from the first nonoscillating part of the eq 11. Quantitative Kinetics Figure 1 demonstrates the enhancement of the radical pair recombination probability induced by the presence of nitroxide radicals. Such behavior of the recombination probability implies that there are two coexisting pathways of the radical pair spin transformation: the “native”, induced by intrapair magnetic interactions (hyperfine, Zeeman, dipolar, etc.) and the catalytic, provoked by nitroxides. Scheme 4 summarizes these two spin transformation channels in terms of kinetic rate constants. The direct transformation of the radical pair, RP, into the recombination product N with the rate constant r is accompanied by catalytic conversion, which includes the entering of the nitroxide radical R into the RP with a diffusional rate constant k0 and the following transformation of the radical triad into the recombination product N with the rate constant r*. The process of diffusional dissociation of RP and the radical triad, which destroys both of them, should also be considered and is supposed to be characterized by the rate constant d. Within the scope of the Scheme 4 the recombination probability PRP along the first noncatalytic pathway is given by the expression
PRP ) r/(r + d + k0[R])
(13)
The probability Ptr of the transformation of the RP within the radical triad is
Ptr ) k0[R]/(r + d + k0[R])
(14)
and the probability for the triad to be transformed into the reaction product N is
Ptr* ) r*/(r* + d)
(15)
Finally, the total radical pair recombination probability P obeys the equation
P ) PRP + PtrPtr*
(16)
By substitution of eqs 13-15 into eq 16, it is easy to derive
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TABLE 2: Ratios r*/r for Lanthanide Ions ion
spin Si
r*/r
ion
spin Si
r*/r
La3+ Ce3+ Pr3+ Nd3+ Pm3+ Sm3+ Eu3+ Gd3+
0 1/2 1 3/2 2 5/2 3 7/2
0 0.34 0.28 0.71
Tb3+ Dy3+ Ho3+ Er3+ Tm3+ Yb3+ Lu3+
3 5/2 2 3/2 1 1/2 0
0.93 0.78 0.62 0.47 0.31 0.31 0
0.93 0 3.4
SCHEME 4: Kinetic Presentation of Radical Pair Reactions
SCHEME 5: Kinetic Presentation of Recombination of Alkyl Radicals R with Nitroxide Mono- and Biradicals
Figure 6. Ratios of the catalytic/noncatalytic rate constants of the radical pair recombination, r*/r, as a function of spin Si of lanthanide ions. Both r* and r refer to the radical pair recombination in amagnetic field of 2000 G.14
negligible. Combining the Scheme 5 with reactions 2kB
B + R 98 M kM
M + R 98 stable products one can derive following expressions for phenomenological rate constants kM and kB:
the final equation
P)
k0[R] r* r + r + d + k0[R] r* + d r + d + k0[R]
(17)
At [R] ) 0 the magnitude of P equals 0.033 (see Figure 1), so the ratio r/d ) 0.033. Thus, the relation r , d reduces eq 17 to
P)
k0[R] r* r + d + k0[R] r* + d d + k0[R]
kM )
k0r k0r*t k0r + ; kB ) r+d (d + t + r)(d + t) d + t + r
Taking into account evident relations r , d, r* , d, t , d, one can derive from eq 19 the ratio of rate constants of spincatalyzed and spin-uncatalyzed RP recombination:
r*/r ) (φ - 1)(d/t) (18)
The quantitative fitting of experimental data to eq 18 shown in Figure 1 results in the ratio r*/r ) 6.3 ( 0.1, which is not sensitive to the rate constant k0 ranging in reasonable diffusional limits of 1010-108 M-1 s-1. The ratio r*/r ) 6.3 is the quantitative measure of spin catalytic efficiency and demonstrates that the rate constant of the RP recombination in the triad is almost an order of magnitude higher than that of the isolated RP. Now we will analyze quantitatively the spin catalysis in the reaction of the nitroxide biradicals with alkyl radicals.11 Scheme 5 describes the sequence of elementary steps in the scavenging of alkyl radicals R by nitroxide monoradical M and biradical B. It implies the encounter between M and R, resulting in the pair (M‚‚‚R), which is able to recombine into the reaction product X or dissociate with the rate constant d. The reaction between B and R includes the encounter pair (M‚‚‚R) with one of the biradical termini. The pair can dissociate and recombine (with rate constants d and r, respectively) or it can be transformed into the triad (B‚‚‚R) if the other terminus of the biradical enters into the radical pair (M‚‚‚R) with the rate constant t. The triad is assumed to recombine, resulting the monoradical M, or dissociate by escaping from the alkyl radical or one of the biradical termini. Note that Scheme 5 does not consider the direct formation of triad (B‚‚‚R) via encounter of R with B. The reason for that is that nitroxide biradicals in Scheme 2 are mostly in extended molecular conformations in which biradical termini are distant so that the probability of the encounter of the alkyl radical with the geminate conformation of B, when both biradical termini are drawn together, is
(19)
(20)
where φ is the ratio kB/kM. Since extended molecular conformations of biradicals dominate, the rate constant t is expected to be at least an order of magnitude lower than that for the escape of the biradical terminus from the triad (B‚‚‚R). The latter is thought to be of the same order of magnitude as the dissociation rate constant d. From these arguments the relation t , d unambiguosly follows, so from eq 20 one can immediately conclude that r*/r . 1. If we assume the ratio d/t to be within the reasonable limits of 10-20, and φ is known to be in the range 1.1-1.5,11 then the ratio r*/r falls into the range 1-10, in general accordance with that for the radical pair generated by DPP photolysis in benzene, as has been discussed above. The lack of known values t and d (or their ratio) prevents a more careful estimation of the r*/r ratio. Now we address the SC by paramagnetic ions. Figure 2 demonstrates that the addition of lanthanide ions Ln3+ causes an increase in the recombination probability. However, the efficiency of different ions in accelerating the recombination process is far from identical. To differentiate the spin catalytic efficiency of the Ln3+ ions, the kinetic scheme similar to that for organic radicals has been used20 and the equation for the recombination probability as a function of Ln3+ concentration has been derived. The equation is identical with eq 17 with the ion concentration in the micellar phase instead of the concentration of radicals in a solution. The ratios r*i for different lanthanide ions are collected in Table 2 and presented in Figure 6 as a function of the ion spin Si. The figure demonstrates the correlation between the efficiency of the ion as a spin catalyser and its electron spin Si. This correlation clearly and unambiguously indicates, in agreement with theory,15 that the exchange interaction between each
18298 J. Phys. Chem., Vol. 100, No. 47, 1996 of the radical pair partners on one side and the paramagnetic ion on the other side is responsible for the spin-catalyzed RP transformation. The absence of correlation between the efficiency of ions and their magnetic moments pointed out by Turro et al.14 provides additional support in favor of the spin catalysis concept. A kinetic analysis of the spin catalytic effect clearly differentiates spin carriers with respect to their ability to produce a spin transformation of radical pairs. The most effective carriers are found to be organic radicals, i.e., spin cariers with an outer unpaired electron. For these carriers the ratio r*/r ≈ 10, i.e., the presence of the spin catalyzer in the radical pair accelerates the spin conversion of the pair by an order of magnitude. Paramagnetic lantanide ions are much less effective, ratios r*/r fall into the range 0.2-1.0, i.e., the contribution of the spin catalytic effect in the RP spin conversion does not exceed 20-100% of the noncatalytic pathway. The low efficiency of ions as spin catalyzers may be attributed to the inaccessibility of the inner unpaired electrons screened partly by the outer electrons. The only exclusion is Gd3+, which appears to be a highly effective spin catalyzer (r*/r ) 3.5), its efficiency approaching that of organic radicals. The unique status of Eu3+, which possesses six unpaired electrons but shows no spin catalytic effect, has been discussed by Turro et al.14 and may be attributed to the fact that this ion is diamagnetic in its ground electronic state because of the cancellation of spin and orbital magnetic moments (for details see ref 21). Conclusion Spin catalysis as a remarkable property of spin selective reactions is a type of physical catalysis in which the catalyzer acts as a spin converter, violating the spin forbiddance of reactions.22 The radical pair recombination, the low-temperature recombination of spin-aligned hydrogen atoms, and cis-trans isomerization of molecules with double bonds are examples of processes spin catalyzed by paramagnetics. As an illustration of the latter process, we address the kinetics of isomerization of dimethylmaleate into its trans-form, dimethylfumarate.23 The reaction was shown to be strongly accelerated by stable nitroxide radicals (TEMPO and its analogues). Neither decay of nitroxide radicals nor the formation of any byproduct was observed, so this is the case of true paramagnetic catalysis. The activation energy of the catalyzed reaction was shown to be precisely equal to that of a noncatalyzed reaction (i.e., the reaction in the absence of nitroxide radicals). However, the preexponential factor of the catalyzed reaction appears to be 7 orders of magnitudes higher than that of a direct, noncatalyzed reaction.23 Both these arguments are unambiguously in favor of “nonenergetic” physical catalysis, based on the violation of the spin conservation rule. Cis-trans isomerization was shown to occur in the weakly bound paramagnetic complex between the dimethylmaleate molecule and the nitroxide radical. By measurement of the NMR paramagnetic shifts and line broadening, it was shown that in the complex the transfer of the spin density of an unpaired electron from the nitroxide radical to the double bond of the ligand molecule takes place.23 The transferred π-electron spin density in the double bond is 2 × 10-3. Spin catalysis is supposed to manifest itself in the twisted conformation of the molecule. In this conformation singlet and triplet states of two π-electrons are energetically degenerate, so the pair of these electrons in cooperation with the third unpaired electron of the radical catalyzer may be considered as a spin triad. Spin conversion in this triad drastically increases the probability of the nonadiabatic reaction pathway along the
Buchachenko and Berdinsky triplet potential energy surface. The difference in these probabilities for the catalyzed and uncatalyzed reaction reaches 7 orders of magnitudes in favor of the former.23 Spin catalysis is supposed to be an important factor that limits or, probably, even prevents observation of the most interesting collective properties of spin-polarized hydrogen atoms and, in particular, the observation of Bose-Einstein condensation of this boson gas.24-26 To detect this phenomenon, the lowtemperature spin-polarized atomic gas compressed to high density is required. However, three-body recombination, in which the leading role has been shown to belong to dipolar and exchange coupling in three-spin triads of polarized hydrogen atoms, results in the generation of hot hydrogen molecules and ultimately in the heating of the gas and decay of the hydrogen atoms, preventing Bose condensation. The theory of spin catalysis15 predicts that even a single nonpolarized hydrogen atom in the polarized gas is enough to catalyze the fast, explosive, nonthreshold hydrogen atom recombination so that it is hardly able to overcome the high-density barrier to Bose condensation of spin-polarized hydrogen atoms. As a mechanism of the radical pair spin conversion, spin catalysis is competitive with the magnetically induced spin conversion and, therefore, results in suppression of the magnetic field effect in the radical pair reactions. This effect has been clearly illustrated by Shkrob et al.27 in the photolysis of deoxybenzoin and its derivatives in SDS micelles. Moreover, the efficiency of lanthanide ions in suppression of the magnetic field effect was found to follow their spin catalytic efficiency. It is worthy to note that the transition metal ion Mn2+ as a spin catalyzer is comparable with Gd3+. The quantitative hierarchy of spin carriers with respect to their spin catalytic efficiency is in excellent agreement with the theory, which predicts that the rate of spin conversion in the radical pair has to be proportional to the difference ∆J of exchange energies between the spin catalyzer and each of the radical pair partners.15 This statement undoubtedly implies that spin carriers with outer unpaired electrons are much more preferable as spin catalyzers than those with inner unpaired electrons. However, although the former spin carriers are effective spin catalyzers, they are usually also chemically reactive radical scavengers, whereas the latter carriers, being rather low efficient spin catalyzers, may be chemically inert. The strategy of spin catalysis is indeed a compromise between these two functions of spin carrier, to be simultaneously spin catalyzer and spin scavenger. Acknowledgment. Financial support of the Russian Fund for Fundamental Research is gratefully acknowlegded (Grant 96-03-34193). References and Notes (1) Salikhov, K. M.; Molin, Yu. N.; Sagdeev, R. Z.; Buchachenko, A. L. Spin Polarization and Magnetic Effects in Radical Reactions; Elsevier: Amsterdam, 1984. (2) Buchachenko, A. L.; Frankevich, E. L. Chemical Generation and Reception of Radio- and MicrowaVes; VCH Publishers: New York, 1994. (3) Steiner, U. E.; Ulrich, T. Chem. ReV. 1989, 89, 51. (4) Sagdeev, R. Z.; Salikhov, K. M.; Leshina, T. V.; Kamkha, M. A.; Shein, S. M.; Molin, Yu. N. JETP Lett. 1972, 16, 599. (5) Buchachenko, A. L.; Galimov, E. M.; Ershov, V. V.; Nikiforov, G. A.; Pershin, A. D. Dokl. Acad. Nauk SSSR 1976, 228, 379. (6) (a) Bargon, J.; Fisher, H.; Johnson, U. Z. Naturforsch. 1967, 22A, 1551. (b) Ward, H.; Lawler, R. J. Am. Chem. Soc. 1967, 89, 5518. (7) Fessenden, R.; Schuler, R. J. Chem. Phys. 1963, 39, 2147. (8) Frankevich, E. L.; Pristupa, A. I.; Lesin, V. I. Phys. Lett. 1977, 47, 304. (9) (a) Tarasov, V. F.; Bagryanskaya, E. G.; Grishin, Yu. A.; Sagdeev, R. Z.; Buchachenko, A. L. MendeleeV Commun. 1991, 85. (b) Okazaki, M. J. Phys. Chem. 1988, 92, 1402.
Feature Article (10) Sagdeev, R. Z.; Molin, Yu. N.; Salikhov, K. M.; Grishin, Yu. A.; Dushkin, A. V.; Gogolev, A. Z. Bull. Magn. Res. 1980, 2, 66. (11) Step, E. N.; Buchachenko, A. L.; Turro, N. J. J. Am. Chem. Soc. 1994, 116, 5462. (12) Bartels, D. M.; Trifunac, A. D.; Lawler, R. G. Chem. Phys. Lett. 1988, 152, 109. (13) Buchachenko, A. L.; Step, E. N.; Ruban, V. L.; Turro, N. J. Chem. Phys .Lett. 1995, 233, 315. (14) (a) Turro, N. J.; Lei, X.; Gould, I. R.; Zimmt, M. B. Chem. Phys. Lett. 1985, 120, 397. (b) Sakaguchi, Y.; Hayashi, H. Chem. Phys. Lett. 1984, 106, 420. (c) Basu, S.; Kundu, L.; Chowdhury, M. Chem. Phys. Lett. 1987, 141, 115. (d) Tanimoto, Y.; Kita, A.; Itoh, M.; Okazaky, M.; Nakagaki, R.; Nagakura, S. Chem. Phys. Lett. 1990, 165, 184. (e) Sakaguchi, Y.; Hayashi, H. Chem. Phys. 1992, 162, 119. (15) Buchachenko, A. L.; Berdinsky, V. L. Chem. Phys. Lett. 1995, 242, 43. (16) Molin, Yu. N.; Salikhov, K. M.; Zamaraev, K. I. Spin Exchange. Principles and Applications in Chemistry and Biology; Springer-Verlag: Heidelberg, 1980. (17) Berdinsky, V. L.; Buchachenko, A. L. Kinet. Catal., submitted for publication. (18) Buchachenko, A. L.; Berdinsky, V. L. Russ. Chem. Bull. 1995, 44, 1578. (19) Anisimov, O. A.; Bizyaev, V. L.; Lukzen, N. N.; Grigoryants, V. M.; Molin, Yu. N. Chem. Phys. Lett. 1983, 101, 131.
J. Phys. Chem., Vol. 100, No. 47, 1996 18299 (20) Buchachenko, A. L.; Berdinsky, V. L.; Turro, N. J. Chem. Phys. Lett., submitted for publication. (21) Rabek, J. F., Ed. Photochemistry and Photophysics; CRC Press: Boca Raton, FL, 1991; Vol. IV, p 1. (22) The term spin catalysis sometimes is used to define such phenomena as an enhancement of intensity of spin forbidden optical transitions stimulated by heavy atom molecules or paramagnetics (see, for instance, Minaev B. F.; Agren H. Collect. Czech. Chem. Commun. 1995, 99, 8936; Theor. Chim. Acta 1996, 57, 519). Our opinion is that such a definition is not justified because the term catalysis itself concerns traditionally chemical reactions and has nothing to do with spectroscopic phenomena. (23) Buchachenko, A. L.; Ruban V. L.; Rozantzev E. G. Kinet. Catal. 1968, 9, 915. (24) Kagan, Yu. M.; Vartanyants, I. A.; Shlyapnikov, G. V. SoV. Phys. JETP (Engl. Transl.) 1982, 54, 590. (25) Sprik, R.; Walraven, J. T. M.; Silvera, I. F. Phys. ReV. Lett. 1983, 51, 479. (26) Hess, H. F.; Bell, D. A.; Kochanski, G. P.; Cline, R. W.; Kleppner, D.; Greytak, T. J. Phys. ReV. Lett. 1983, 51, 483. (27) Shkrob, I. A.; Margulis, L. A.; Tarasov, V. F. Russ. J. Phys. Chem. (Engl. Transl.) 1989, 63, 1827.
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